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Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed. (1 point) Responses y=8x y equals 8 x y=x y equals x y=3x y equals 3 x y=33x y equals Start Fraction 3 over 3 End Fraction x

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To derive the equation \( y = mx \) for a line through the origin, we need to determine the slope \( m \) based on the graph you are referring to.

Since I don't have access to the actual graph, I can guide you on how to derive the equation based on the slope you observe:

  1. Identify two points on the line that passes through the origin (0,0).
  2. Use the formula for the slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
  3. If you find that the slope \( m \) equals 8 based on your observations, then the equation is \( y = 8x \).
  4. If the slope \( m \) equals 1, then the equation is \( y = x \).
  5. If \( m \) equals 3, then the equation is \( y = 3x \).
  6. If the slope is 33, the equation will be \( y = 33x \).
  7. If the slope simplifies to \( \frac{3}{3} \), it will simplify to \( 1 \), leading to the equation \( y = x \).

Based on the options you provided, if the slope was determined to be 8, 1, 3, or a repeat of 1 from the simplification of \( \frac{3}{3} \), the responses would be:

  • \( y = 8x \)
  • \( y = x \)
  • \( y = 3x \)

Please choose the correct option depending on the slope of the line you identified.